How to set two different HDRI, one for environment lighting, and another for background, in 2.8 using Eevee?
To render a different background than the one used in the environment

Just enable Film>Alpha>Transparent.

Then on the compositor use Alpha over to mix over the background you want to use.



Alternatively you can use a background for the world that is only seen by the camera and not by other rays, therefore not contributing to the lights, reflectons,etc.

Set two different Environment background shaders and use the Is Camera Ray from a Light Path node to control the shader mix.